We present a new approach for the stability analysis of linear coupled differential-difference systems with a general distributed delay. The distributed delay term in this note can contain any L2 function which is approximated via a class of elementary functions including polynomial, trigonometric, exponential functions, etc. Through the application of a new proposed integral inequality, a sufficient condition for the stability of the system is derived in terms of linear matrix inequalities based on the construction of a Lyapunov Krasovskii functional. The methods proposed in this note can handle problems that cannot be dealt using existing approaches. Two numerical examples are presented to show the effectiveness of our proposed stability condition.

中文翻译：

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具有一般分布时滞的线性耦合微分系统的稳定性分析


我们提出了一种新的方法来分析具有一般分布延迟的线性耦合微分系统的稳定性。本文中的分布式延迟项可以包含任何 L2 函数，该函数通过一类初等函数（包括多项式、三角函数、指数函数等）来近似。通过应用新提出的积分不等式，系统稳定性的充分条件是根据基于 Lyapunov Krasovskii 泛函构造的线性矩阵不等式导出的。本文提出的方法可以解决使用现有方法无法解决的问题。两个数值例子展示了我们提出的稳定性条件的有效性。